Simple and compound interest

Want to know everything about simple and compound interest? So you are in the right place. In this matter, you will understand what they are, what the formula is and how to calculate each one of them.

Don’t worry if you still don’t know the difference between simple and compound interest, as this question is very common. First of all, you need to know that simple and compound interest is not always the villain in your pocket. Knowing how to use them, they can be a great ally to your finances.

What are interest?

The word interest means an amount of money more applied in some financial operations. During your lifetime, you can either pay or receive interest, depending on the type of financial investment you make. 

Got confused? Let’s look at examples of when you pay interest and when you earn interest.

When you pay interest

When delaying the payment of a bill, interest is charged for the delay, that is, an amount more than what you would initially pay. This extra charge is a kind of compensation for the period in which someone (usually the financial institution) bore the loss of the delay.

In this case, the idea behind charging interest works like this: when the bill is not paid, the company that sold the product or service is doubly at a loss. First, because the company delivered the product/service, but did not receive the combined amount. Second, because it loses the chance to raise extra money, an amount that could have profited if it had invested the money it did not receive.

Now that we touch on the subject of investment, it is easier to understand the situations in which we receive simple and compound interest.

When you earn interest

When a person makes an investment, he receives interest for “lending” money to the bank or a company. In this situation, interest is also called income.

Here, the logic works this way: you have money sitting in savings. The bank borrows the amount you deposit to make other transactions, while you don’t need the money — so, in theory, the longer your money sits still, the more it yields. 

A similar situation occurs when buying shares of a company on the stock exchange. In practice, you are “lending” money to the company to buy inputs, hire more employees, etc.

For each credit, loan-to-value ratio or investment operation, a different interest rate is applied. For example, the interest on a revolving credit card is very different from the interest on a secured loan. 

When it comes to investments, the interest paid to those who put their money in savings accounts is absolutely different from those received by those who invest in stocks traded on the stock exchange. 

Now that you know what interest is, you can better understand the importance of the concept of simple and compound interest and the difference between the two types.

What are the differences between simple and compound interest?

Knowing what interest is, we can now better understand why some financial transactions use simple interest and others use compound interest.

In general, simple interest is calculated according to the total amount of the operation and is more common in daily transactions. Compound interest, also called interest on interest, is calculated on the total value of the operation + the value of simple interest, and is common in long-term investments.

Let’s take a closer look at each of them and understand how each calculation is done.

What is simple interest

Simple interest is more present in everyday financial transactions. It is used, for example, on credit cards, financing and some types of loans.

Unlike its “brother” compound interest, the value of simple interest never changes during an operation. Thus, if you signed a contract with a certain percentage of interest, you will pay or receive this amount until the end of the contract. 

Let’s see an example:

You have R$1000 to keep for the future, money that you don’t intend to use in the coming months. To make this amount grow, you choose an application with a simple interest rate of 5% per month, which means that, every month, you have an income of R$ 50. Thus, from the first month you will have R$ 1050 on the bill. In the second month, R$ 1100, and so on.

Interest works like yeast when making bread, increasing the size of the dough (in this case, your money) and increasing the number of buns.

simple interest formula

If you are familiar with mathematics, it is possible to apply a simple interest formula that is not very complex to calculate its final value.

See the formula for you to calculate and know how much you will pay in simple interest on an operation: 

  • C x I ÷ 100 x T = J

To make the calculation easier, replace the letters with the respective numbers:

  • In , enter the amount of capital provided for in the contract, that is, how much you will pay (in a loan) or deposit (in an investment).
  • In , place the value of the simple interest rate agreed in the contract.
  • In , enter the time provided for in the contract.

At the end of the multiplication and division accounts, you will know the value of J, that is, how much interest you will pay on this transaction. This will help you to know the total amount you will pay on a loan, for example.

Here is an example of a loan of R$900 to be paid off in six months at a simple interest rate of 5% per month:

  •  900 x 5 ÷ 100 x 6 = 270 

This means that at the end of six months, the total amount spent on the loan will be R$1170 (R$900 of borrowed capital + R$270 of interest). 

What is compound interest

The most relevant difference between simple and compound interest is time. In financial operations based on simple interest, time is not very important, since the final amount paid will be the same, regardless of the term. 

When compound interest is applied to the transaction, the term makes all the difference, because the longer the time to pay off a loan, the more interest will be paid, since the rate is calculated on top of the accumulated debt.

In this case, compound interest is an excellent ally in long-term investments. Here’s how to make the account:

compound interest formula

For those who enjoy math, there is a compound interest formula that simplifies calculating its value.

Calculating compound interest is a bit more complicated than simple interest. In case you get confused by the lyrics, don’t worry, we also made a glossary right after that to help you out. 

  • C x (1 + I ÷100) T = M
  • In , enter the amount of capital provided for in the contract, that is, how much you will pay (in a loan) or deposit (in an investment).
  • In , place the value of the simple interest rate agreed in the contract.
  • In , enter the time provided for in the contract.
  • is the result of sums, multiplications and divisions, the total amount of what you will pay already with compound interest.

See an example of a BRL 50,000 loan (C) to be paid in two years (T) at an annual rate of 12% (I):

  • 50,000 x (1 + 12 ÷ 100) 2 = M
  • 50,000 x 1.2544 = 62,720

That is, at the end of 24 months you will have paid back the R$50,000 you borrowed + R$12,720 in interest.

Simple or compound interest: which is applied in loans?

Loan contracts usually work with compound interest. This is interest charged on interest. 

Simple interest can also be used in loan operations, usually when the term is shorter. However, there are few operations that opt ​​for the simple interest regime. Currently, the financial system uses compound interest more.

Therefore, if you apply for a loan at the bank or with any financial institution, you will probably pay compound interest. Even so, there are low-interest loan types , such as those where you leave a good as collateral: real estate refinancing , vehicle refinancing and payroll loans are among the most common types.

It is possible to estimate the value and number of installments for your credit in different modalities using the loan simulator below. Just enter the amount you want to borrow, plus the number of months to pay.

Do you understand how to calculate simple and compound interest? 

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